What are the odds?

[sg]

I chose this category to post in a hope that I would get answers from mathematical , probability solving type people.
I play the game Words With Friends (unofficial Scrabble) on my phone and always have the maximum number of games going. The other day I realised the seven tiles the game had generated for me were the letters in my surname.
Can anyone work out roughly what the chances are of that?

[Celticv11]

657,800

[Celticv11]

http://www.google.co....STWQ_dUKv8bJ2NT8phUA. Easy

[dr b]

celtic's answer is correct if you are asking: my last name is ABCDEFG; what are the odds of drawing those letters at random from a bag containing the letters ABC...XYZ?

But, doesn't it also depend on the probability of drawing a certain letter? There is on;t one Z in a Scrabble set but many E's. So if you last name is ZAXJAQK, the probability would be far lower than if it was DEARTIS.

[dr b]

^"only one Z"

[sg]

That's brilliant, thanks! Ok my seven letter surname contains vowels I, E A, and consonants R, L, Z, G - I don't really mind if you work out the name, but can you calculate that probability?

[Celticv11]

Dr b. correct , many variables. 657,800 refers to having the alphabet in a bag, any 7 from 26

[Celticv11]

And then calculate the odds of them being drawn in the correct order? :)

[dr b]

Ok, so there are 98 tiles in a scrabble set, of which you have:

9 I
12 E
9 A
6 R
4 L
1 Z
3 G

Prob of drawing an I is 9/98; prob of drawing an E is 12/97 (only 97 tiles left after you draw first), prob(A) = 9/96 ... prob (G) = 3/92. The Z kills you since there is only one in the set.

Changing the required order of draws would affect the total probability only slightly (any of these numbers divided by 98, 97, 96 etc are pretty much the same).

So the probability = (9/98) x (12/97) x ... x (3/92) = 1.003 x 10^-9. A very slim chance!!

[dr b]

actually changing the required order of the draws changes the probability not at all!

[dr b]

If your last name consisted of the 7 most popular letters (E, O, A, I, T, R, N) the probability would increase to a whopping 2.409 x 10^-8.


I will go away now.

[mojay]

I felt a bit like that last week in the local co-op - when she held out her hand for money and quoted my pin number :)

[pdust]

brill thread and hi sg :)

[sg]

Wow! That's mind boggling! And hi pix! What's the probability of you remembering my surname?!

[pdust]

i can remember it easily lol and your first name